Displaying similar documents to “A classification theorem for nuclear purely infinite simple C * -algebras.”

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

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We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the...

A double commutant theorem for purely large C*-subalgebras of real rank zero corona algebras

P. W. Ng (2009)

Studia Mathematica

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Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.

Unital extensions of A F -algebras by purely infinite simple algebras

Junping Liu, Changguo Wei (2014)

Czechoslovak Mathematical Journal

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In this paper, we consider the classification of unital extensions of A F -algebras by their six-term exact sequences in K -theory. Using the classification theory of C * -algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of A F -algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of A F -algebras by stable purely infinite simple C * -algebras...